Constraint propagation in N+1-dimensional space-time

Abstract

Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for future numerical research of higher-dimensional space-time, we study the dimensional dependence of constraint propagation behavior. The $N+1$ Arnowitt-Deser-Misner evolution equation has matter terms which depend on $N$, but the constraints and constraint propagation equations remain the same. This indicates that there would be problems with accuracy and stability when we directly apply the $N+1$ ADM formulation to numerical simulations as we have experienced in four-dimensional cases. However, we also conclude that previous efforts in re-formulating the Einstein equations can be applied if they are based on constraint propagation analysis.

4 pages, to appear in Gen. Rel. Grav

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Cited by in corpus (5)

• $N+1$ formalism in Einstein-Gauss-Bonnet gravity
• Constraint propagation equations of the 3+1 decomposition of f(R) gravity
• Formation of naked singularities in five-dimensional space-time
• On the Hyperbolicity and Stability of $3+1$ Formulations of Metric $f(R)$ Gravity
• On constraint preservation and strong hyperbolicity